Relating Velocity vs. Time Graphs to Position vs. Time Graphs: Constant Velocity

Although physics requires numerous calculations and formulas to solve problems, many introductory physics students face challenges understanding the concepts behind the calculations.  One of the common concepts encountered by beginning physics students is the position vs. time graph and the velocity vs. time graph.

A good review for the position vs. time graph and the velocity vs. time graph can be found at the physics classroom website (click here).  What I would like to focus on in today’s blog lesson, is correlating a velocity vs. time graph to a position vs. time graph.

The slope of a line plotted on a position vs. time graph is the object’s velocity.  Then, velocity can be graphed on the y-axis with time on the x, and the slope of this new graph is an object’s acceleration.

So if an object exhibits a straight horizontal line such as in the velocity vs. time graph that follows, what would the object’s motion look like on a position vs. time graph?

A straight horizontal line on a velocity vs. time graph is a line with no slope and signifies an object with constant velocity.  As such, this object has no change in velocity and therefore with a slope of zero, has no acceleration.    A constant positive velocity as depicted on a position versus time graph looks like a straight line, inclined at an angle.

An object with a constant negative velocity would have a negative slope when graphed on a position versus time graph.

 

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